Sub-annular structure in black hole image from gravitational refraction

The images of supermassive black holes captured by the Event Horizon Telescope (EHT) collaboration have allowed us to have access to the physical processes that occur in the vicinity of the event horizons of these objects. Furthermore, black hole imaging gives rise to a new way of testing general relativity in the strong field regime. This has initiated a line of research aimed at probing different physical scenarios. While many scenarios have been proposed in the literature that yield distortion effects that would be a priori detectable at the resolution achieved by future EHT observations, the vast majority of those scenarios involve strange objects or exotic matter content. Here, we consider a less heterodox scenario which, involving non-exotic matter, in the sense that it satisfies all energy conditions and is dynamically stable, also leads to a deformation of the black hole shadow. We consider a specific concentration of non-emitting, relativistic matter of zero optical depth forming a bubble around the black hole. Due to gravitational refraction, such a self-interacting—dark—matter concentration may produce sub-annular images, i.e. subleading images inside the photon ring. We calculate the ray tracing in the space-time geometry produced by such a matter configuration and obtain the corresponding black hole images. While for concreteness we restrict our analysis to a specific matter distribution, modeling the bubble as a thin-shell, effects qualitatively similar to those described here are expected to occur for more general density profiles.